Question

How do you find an angle with a positive measure and an angle with a negative measure that are coterminal with `50^circ`?

Answer 1

`A_c = A + k xx 360^o`
`A_c = 50 + 360^o = 410^o` (or `50^o`) and
`A_c = 50 - 360^o = -310^o`

Explanation:

Coterminal angles `A_c` to angle A may be obtained by adding or subtracting `k xx 360` degrees or `k xx (2 Pi)`. Hence,

`A_c = A + k xx 360^o` if A is given in degrees.

or

`A_c = A + k xx (2pi)` if A is given in radians.

where k is any negative or positive integer.

A couple of good tutorials are here:
http://www.analyzemath.com/Angle/coterminal_angle.html

http://www.mathwarehouse.com/coterminal-angle/how-to-calculate-coterminal-angles.php